A small finite universe and some wierd thoughts from it

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SUMMARY

The discussion revolves around the topology of the universe, specifically the concept of a finite universe resembling a 3D torus or a balloon's surface. The user explores the implications of a small universe where one could see multiple copies of oneself due to the universe's repeating nature. A referenced paper discusses using the cosmic microwave background (CMB) to measure the universe's topology, proposing that in a 3D toroidal universe, one could observe multiple copies of the CMB sky. The study aimed to identify intersecting circles in the CMB but did not find conclusive evidence, leaving the question of the universe's topology open for further exploration.

PREREQUISITES
  • Basic understanding of cosmology and the big bang theory
  • Familiarity with the concept of the cosmic microwave background (CMB)
  • Knowledge of topological concepts, particularly in relation to 3D shapes
  • Ability to interpret scientific papers and diagrams
NEXT STEPS
  • Read the paper on cosmic microwave background topology: arXiv: astro-ph/9801212
  • Explore the implications of a 3D toroidal universe and its observational consequences
  • Investigate the methods used to analyze the CMB for signs of topology
  • Study the mathematical principles of topology as they apply to cosmology
USEFUL FOR

Astronomers, cosmologists, and physics enthusiasts interested in the structure and topology of the universe, as well as those exploring the implications of the cosmic microwave background in cosmological studies.

JHUK
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I do not have physics education pass A-levels, yet. So what I've been thinking of should be very simple to follow. It's just so fascinating that I'm wondering if any experts could either point a logic flaw, or direct me to material that has already mused over this for me.

I understand that the answer to "what is at the edge of the universe" is something we can't know, due to the limited distance that light has traveled since the big bang. But that it's speculated that the universe is like a 3D version of a balloon's surface, that if you were to travel far enough in one direction, you'd end up back where you begin.

This brings up the very interesting and fun question, to imagine a universe like this being only the size of a small room. You're floating, what do you see? (we can assume there's light, air, etc for our convenience) Naturally you'd see the back of yourself. Now twist forward (shrink the universe a bit for this) and grab hold of "his" leg, you'd feel the same hand wrap around your own leg. There's a lot of funny things you could do here.

But on further reflection, if the universe "repeats" itself in front of you, it should also do it upwards. But likewise it should also "repeat" in any direction, which begins creating an absurd and confusing scenario, so to simplify it, imagine just a sphere.

Place this imagined sphere inside this empty and small universe. Wherever it is, we can picture that as the "center" (e.g. like placing a dot onto a balloon containing no other drawings). For our convenience, this sphere is also able to see, and emit light.

I'm going to get a sphere picture from google images, and express the rest using a crude MSpaint diagram.

pBTFv.png


You get a similar result if you picture a point on an empty sphere. If you imagine light travels over the surface like everything else, instead of flying off into space, light emitted from the point would fly around the planet and hit it's back. The point would therefore see a circle around him. Made of him.
 
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Great post JHUK! It looks like you're having some fun with the topology of the universe. If you're interested, check out this paper:

http://arxiv.org/abs/astro-ph/9801212"

These guys seek to use the cosmic microwave background to measure the topology of the universe. Rather than a sphere, they consider the case in which the universe is a 3D torus (a cube with opposite faces identified). Now, rather than a person seeing copies of himself in every direction (as in the case of the sphere), one sees copies of himself in 4 directions. In this paper, the authors are interested in what the CMB looks like in such a universe. As you may know, the CMB is seen as a 2D sphere, called the surface of last scattering. In the paper, they imagine the case in which the distance to the last scattering surface is larger than the dimension of the cube. Then, what one sees is 4 intersecting copies of the CMB-sky:

http://member.ipmu.jp/brian.powell/cmb.jpg

The task is then to go and look for the circles of intersection -- giant rings in the CMB sky. Their study didn't find any such rings, but I think the book is still open on the topology of the universe!
 
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